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Simplifying 0 = 5x2 + 15x + -10 Reorder the terms: 0 = -10 + 15x + 5x2 Solving 0 = -10 + 15x + 5x2 Solving for variable 'x'. Combine like terms: 0 + 10 = 10 10 + -15x + -5x2 = -10 + 15x + 5x2 + 10 + -15x + -5x2 Reorder the terms: 10 + -15x + -5x2 = -10 + 10 + 15x + -15x + 5x2 + -5x2 Combine like terms: -10 + 10 = 0 10 + -15x + -5x2 = 0 + 15x + -15x + 5x2 + -5x2 10 + -15x + -5x2 = 15x + -15x + 5x2 + -5x2 Combine like terms: 15x + -15x = 0 10 + -15x + -5x2 = 0 + 5x2 + -5x2 10 + -15x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 10 + -15x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(2 + -3x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2 + -3x + -1x2)' equal to zero and attempt to solve: Simplifying 2 + -3x + -1x2 = 0 Solving 2 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + 3x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 3x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 3x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3x + x2 = 0 + 2 3x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 3x + x2 = 2 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 2 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 2 + 2.25 Combine like terms: 2 + 2.25 = 4.25 2.25 + 3x + x2 = 4.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + 1.5) equal to 2.061552813 and -2.061552813.Subproblem 1
x + 1.5 = 2.061552813 Simplifying x + 1.5 = 2.061552813 Reorder the terms: 1.5 + x = 2.061552813 Solving 1.5 + x = 2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.061552813 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.061552813 + -1.5 x = 2.061552813 + -1.5 Combine like terms: 2.061552813 + -1.5 = 0.561552813 x = 0.561552813 Simplifying x = 0.561552813Subproblem 2
x + 1.5 = -2.061552813 Simplifying x + 1.5 = -2.061552813 Reorder the terms: 1.5 + x = -2.061552813 Solving 1.5 + x = -2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.061552813 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.061552813 + -1.5 x = -2.061552813 + -1.5 Combine like terms: -2.061552813 + -1.5 = -3.561552813 x = -3.561552813 Simplifying x = -3.561552813Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.561552813, -3.561552813}Solution
x = {0.561552813, -3.561552813}
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